A Topological field model of a circular ribbon flare

A flare (M1.1) on 2000-Mar-17 at 11:25 was characterized by TRACE observers as a "circular ribbon flare" (see the TRACE Flare Catalog). More commonly flare ribbons (observed in chromospheric emission) form two distinct bands --- a morphology to which they owe their name. This two-ribbon configuration has been succesfully explained by solar flare theories appealing to magnetic reconnection at a magnetic X-point or neutral point. Such reconnection theories are intrisically two-dimensional: theoretical arguments suggest that neutral points are far too uncommon in three-dimensional fields to be a necessary pre-condition for events as common as two-ribbon flares. Nor could such a model explain a single circular ribbon.

A related class of models predict that three-diemnsional reconnection will occur at topological magnetic field boundaries called separators and separatrices. To test this hypothesis MURI team members Dana Longcope and Terry Forbes worked with Leon Golub, while at the Intitute for Theoretical Physics, to develop a topological field model of the flare 2000-Mar-17.

The topology of the field is defined by how photospheric sources are interconnected. The first step in a topological model is an identification of photospheric sources by grouping concentrations in a magnetogram. This was done by extracting NOAA 8906 from a full disk MDI magnetogram made at 11:20.

A total of 62 sources (34 positive, 28 negative) were identified. The sub-region in the vicinity of the flare shows a lone positive source (P10) next a stong cluster of negative sources (N35 - N38) and an arc of weaker negative sources.

The Chromospheric structure

The chromospheric emission (shown in these 1600 A images from TRACE) shows the ribbons. The earliest image (11:10) shows two distinct features, akin to a traditional two-ribbon flare. This develops into a circular ribbon extending from near P10 along much of the negtive arc. The question remains "Is this related to a spearatrix?".

The Coronal structure

A sequence of coronal images made by TRACE at 195 A shows the structure of the coronal magnetic field lines. At early times (11:22 -- 11:27) the field lines resemble spokes eminating from a central point.

This resemblence fueled early speculation that this was one of the supposedly rare regions whose magnetic field has a null point high in the corona. If this were the case all field lines would connect to photospheric sources of the same sign. The rim of this wheel consists of a positive source (P10) in addition to many nagatives. In later coronal images the hub-and-spoke morphology evolves into two systems of simple arches which appear to cross near the center. The loops in each set of arches seem to connect points near P10 to points near N36/N37: the connect positive to negative as any magnetic field line should.

An intermediate time shows a rather different structure whose relation to the arches is unclear.

Is it a speratrix?

A model of the coronal magnetic field is constructed by first replacing each photopsheric source by a point magnetic charge with equivalent flux, located on a plane tangent to the phtosphere. One model matching this source distribution is that of a potential field --- a magnetic field without current. This field contains a separatrix surface overlying P10 (the surface is indicated by a set of field lines from it).

in this field P10 connects to negative sources N35 -- N38 but to none of the outlying arc.

There is a separator field line (red) connecting photospheric footpoints B01 to A03 (yellow) --- these could be contrued to be the initial two ribbons seen in the 11:10 chomospheric image. Reconnection at this separatirx would disconnect field lines from positive source P27 (outside) and reconnect them to P10 (inside). After undergoing such a reconnection episode a field line would find itself just underneath the separatrix, connected to P10. (see green field lines). Do the coronal loops resemble such newly reconnected field lines? The photospheric footprint of the separatrix (blue) does not include the outlying negative arc. How could the circular chromospheric ribbons be explained?

A linear force-free field provides a second coronal field model. In this example the current density is assumed to be proportion to the magnetic field with a constant of proportionality of +0.012 Mm^-1 (not an atypical value for an active region). The force-free field contains a separatix corresponding to the one in the potential field, but somewhat distorted by currents.

A notable improvement is that P10 connects to all of the negative sources in the arc. Furthermore, the model field lines bend to the right as do the coronal loops.

In the future the same topolical field modeling technique will be applied to MURI's case study flares in AR 8210,

MURI-MSU Nugget June 2002

Stéphane Régnier, Richard Canfield, Dana Longcope